Method of regulating and controlling a technical process such as spot-welding of metal sheets

ABSTRACT

A method for controlling and driving a technical process executed in time by applying at each time t instructions Ci(t), leading to a measurable but not observable result R(t) and generating a plurality of observable quantities distinct from the result R(t) whereof at least two are independent Gj(t), which consists in: measuring at least two independent observable quantities Gj(t), Gp(t); with a predictive model M, or a set of models, whereof the variables comprise the at least two independent observable quantities, calculating an estimation Res(t)=M(G1(t), Gp(t) of the result R(t); using a drive law L, whereof the input variable is the estimated result Res(t) calculating new instructions Ci(t+1), applicable for time t+1; and replacing the instructions [C1(t), Cn(t)] by the instructions [C1(t), Cn(t+1)]. The method for controlling and driving a technical process is applicable to spot welding.

FIELD OF THE INVENTION

The present invention relates to a method of regulating and controllinga technical process which is executed in time either in a continuousmanner or in a discontinuous manner, the process being in particularspot-welding of an assembly of metal sheets.

DESCRIPTION OF RELATED ART

The technical processes which can be regulated and controlled by controlsystems are very varied and are to be found in all industries. Ingeneral, a process transforms an object, characterised by quantitieswhich are input quantities for the process, into another objectcharacterised by quantities which are output quantities for the process.The execution of the process can be controlled by desired quantitiescorresponding to regulating parameters fixed by an operator or by acontrol system. Also in general, it is desired that at least one outputquantity should remain close to an intended value, and it is then saidthat this quantity is regulated. In order to achieve this objective,that is to say obtaining an output quantity having a value close to theintended value, the desired quantities are adjusted. The adjustment ofthe desired quantities on the basis of the measurement of characteristicquantities of the process, as well as the use of these measurements formonitoring the execution thereof, constitutes the method of regulatingand controlling the process. It should be noted that, if the outputquantities are variables which are independent of one another, it isonly possible to regulate one and only one of these quantities. It willtherefore be assumed in the following that only one output quantity isregulated, even if the process can be characterised by several outputquantities which are independent of one another. In the following theoutput quantity to be regulated will also be called the “result”.Finally, the execution of the process may in general be characterised byquantities linked to the phenomena brought into play by the process;these quantities are neither input quantities nor output quantities.

An input or output quantity, or any other quantity associated with theprocess, may or may not be measured and, if it may be measured themeasurement may or may not be carried out in real time withoutdisrupting the process. In the following:

-   -   “Measurable quantity” will be used to mean a quantity which can        be measured, that is to say to which it is possible to make a        numerical value correspond; such a quantity is not necessarily        measurable in real time.    -   “Observable quantity” will be used to mean a measurable quantity        which can be measured directly on the process or on the product        directly resulting from the process, in real time.

Methods for regulating and controlling a process are known for examplewhich consist of measuring the output quantity to be regulated,comparing this measurement with the intended value then, using a controllaw, modifying the desired quantities. Such a process assumes that theoutput quantity in question can be measured in real time.

In a variant of the preceding method, the quantity to be regulated isnot measurable in real time but is correlated in a known manner withanother output quantity which is itself measurable in real time. In thiscase the quantity to be regulated is replaced by the measurable outputquantity and this latter quantity is adjusted.

Methods for regulating and controlling a process are also known whichconsists of measuring the input quantities and calculating the desiredquantities using a model of which the variables are the measured inputquantities and the intended output value. This model then constitutesthe control law; it does not permit calculation of a forecast value forthe output quantity to be regulated. Such a process assumes that it ispossible to measure the input quantities and that a suitable model isavailable.

Methods of regulating and controlling a process are also known whichconsist of measuring the input quantities, calculating with the aid of apredictive model, the variables of which are the input quantities andthe desired quantities, an estimate of the value of the output quantityto be regulated, comparing this estimate with the intended value andusing this comparison in order to modify the desired quantities using adrive law. Such a process assumes that the input quantities can bemeasured in real time and that a suitable predictive model is available.

Finally, methods of regulating and controlling a process are known whichuse a model permitting calculation, on the basis of the output quantityto be regulated and the desired quantities, of the value of an outputquantity which is easy to measure, different from the quantity to beregulated but closely correlated therewith. In this method, on the basisof the intended value for the output quantities to be regulated and thedesired quantities, an intended value is calculated for the outputquantity which is easy to measure, then the measured value of thisquantity is compared with the intended value, and on the basis of thiscomparison the desired quantities are modified using a control law. Thismethod assumes in particular that at least one output quantity which iseasy to measure is known, which can be calculated on the basis of amodel of which the variables are the output quantity to be regulated anddesired quantities.

However, processes exist to which none of these methods of regulationand control are applicable. This is so in particular in the case ofspot-welding of an assembly of metal sheets. In effect, in this processthe result to be obtained can only be measured by a destructive test andcannot therefore be used for continuously regulating and controlling theprocess. On the other hand, the result depends not only upon the inputand desired quantities but also upon the wear on the device used forcarrying out the welding. But no reliable means are known for measuringthe wear on the device. Therefore it is not possible on the basis of theinput and desired quantities to forecast either the quality of the weldnor any other output quantity which, by itself, would be representativeof the quality of the weld. Finally, no output quantity closelycorrelated with the result to be regulated is known.

Therefore there are processes, of which spot-welding is an example, inwhich the input quantities, the output quantities and the desiredquantities do not allow the known methods of regulation to beimplemented.

SUMMARY OF THE INVENTION

The object of the present invention is to remedy this drawback byproposing a means for continuously regulating and controlling atechnical process such as spot-welding in which it is not possible toobserve (in the sense defined above) the result obtained, and for whichthis result cannot be forecast on the basis only of the measurements ofthe measurable input quantities or of one single measurable outputquantity.

Therefore the invention relates to a method of regulating andcontrolling a technical process which is executed in time either in acontinuous manner or in a discontinuous manner by applying at each timet desired values {C₁(t), . . . , C_(n)(t)} leading to a result R(t)which is measurable but not observable which it is desired to keep closeto an intended value R_(v) and generating a plurality of observablequantities of which at least two are independent {G₁(t), . . . ,G_(m)(t)} according to which:

-   -   at least two independent observable quantities G₁(t), . . . ,        G_(p)(t) are measured,    -   with the aid of a predictive model M, or a set of models, of        which the input variables include the at least two independent        observable quantities and possibly at least one desired value        C₁(t), . . . , C_(q)(t), an estimate R_(es)(t)=M(G₁(t), . . . ,        G_(p)(t), C₁(t), . . . , C_(q)(t)) of the result R(t) is        calculated,    -   with the aid of a control law L of which the input variable is        the estimated result R_(es)(t) and the intended result R_(v),        new desired values {C₁(t+1), . . . , C_(n)(t+1)}=L(R_(es)(t),        R_(v)) are calculated which are applicable for the time t+1,    -   and the desired values {C₁(t), . . . , C_(n)(t)} are replaced by        the desired values {C₁(t+1), . . . , C_(n)(t+1)}.

The predictive model M may be a statistical adjustment model dependingupon parameters {θ₁, . . . , θ_(p)} which constitute a parameters vectorθ adjusted on a learning base B_(ap) consisting of all of the desiredvalues, the measurements of the observable quantities and themeasurement of the result for a plurality of successive executions ofthe technical process.

In order to determine the model M it is possible, for example, toproceed in the following manner:

-   -   a model structure is chosen depending upon a parameter vector θ,    -   a cost function J is chosen having for example a quadratic form,    -   with the learning base a succession of adjusted models M_(a,k)        is calculated corresponding to different parameter vectors θ_(k)        of dimension q_(k) which minimise, globally or locally, the cost        function on the learning base,    -   for each model M_(a,k) the coefficients h_(ii) of each of the        examples of the learning base are calculated, and the        generalised score of the model M_(a,k) is calculated:

${E\left( \theta_{a,k} \right)} = {\sum\limits_{{i = 1},N}^{\;}\left\lbrack {\left( {{M_{a,k}\left( {x^{i};\theta_{a,k}} \right)} - R_{i}} \right)/\left( {1 - h_{ii}} \right)} \right\rbrack^{2}}$

-   -   and a quantity

${\mu\left( \theta_{a,k} \right)} = {\left( {N \cdot q_{k}} \right)^{{- 1}/2}{\sum\limits_{i = {1\mspace{14mu}{to}\mspace{14mu} N}}h_{ii}^{1/2}}}$

-   -    is calculated and the model M_(a,k) having the greatest        μ(θ_(a,k)) is chosen from amongst the models having the smallest        E(θ_(a,k)); this model is the optimal model M_(a,opt).

Preferably:

-   -   for the measurement of the result R a dispersion range [σ_(min),        σ_(max)] of the standard deviation of the measuring error is        determined,    -   and the parameters {θ₁, . . . , θ_(p)} of the predictive model M        are adjusted in such a way that on a test base B_(test) it has a        score S such that σ_(min)<S<σ_(max), the test base consisting of        all of the instructions, the measurements of observable        quantities and the measurement of the result for a plurality of        successive executions of the technical process, different from        the learning base.

In order to adjust the parameters {θ₁, . . . , θ_(p)} of the predictivemodel M, it is possible to choose a first learning base B_(ap) and afirst test base B_(test) and to proceed as follows: with the aid of thesaid first learning base a first estimate of the parameters {θ₁, . . . ,θ_(p)} is determined in such a way that the score of the model M for thelearning base is within the dispersion range [σ_(min), σ_(max)], then,using this first estimate of the parameters in the model M, with the aidof the first test base B_(test), the score S is evaluated and comparedwith the dispersion range [σ_(min), σ_(max)]. If S is within the saiddispersion range it is considered that the estimate of the parameters issatisfactory, in the opposite case the learning base B_(ap) is completedwith examples taken from the first test base in order to constitute anew learning base, the test base is completed if need be and theparameters {θ₁, . . . , θ_(p)} are determined again with the aid of thenew learning base and the score S on the new test base, and theiterations are continued until the score S is within the dispersionrange [σ_(min), σ_(max)].

In order to complete the learning base with examples taken from the testbase it is possible:

-   -   to fix a confidence interval threshold Sk for the predictions of        the model,    -   to calculate the confidence interval Ik for prediction of the        model M for each of the examples of the test base,    -   and to introduce into the learning base all the examples of the        test base of which the confidence interval Ik is greater than        Sk.

In the course of the operation of the process, it is possible to measureat least one result and the corresponding observable quantities in sucha way as to determine at least one supplementary example which is addedto the learning base and, with the new learning base thus obtained, toevaluate the performance of the model and, if necessary, adjust theparameters of the model.

The model M is for example a neural network.

The technical process may in particular be spot-welding of metal sheets.

In this case the result R is, for example, the diameter Φ of the weldnugget and the desired values C₁, . . . , C_(n) are the welding forceF_(s), the welding intensity I_(s), the welding time Δt_(s) and theforging time Δt_(f). The observable quantities are, for example, thetotal electrical energy E_(t), the maximum expansion in the course ofwelding Δz_(s) and the maximum contraction during the forging phaseΔZ_(f).

The control law L may be defined in the following way:

-   -   a minimum value Φ_(min) and a maximum value Φ_(max) are chosen        for the diameter of the weld nugget,    -   a number qm is chosen,    -   the moving mean Φ_(mg) of the qm last predictions of the        diameter of the weld nugget Φ is formed,    -   if Φ_(mg)>Φ_(max) the desired value Ic of the welding intensity        is decreased, if Φ_(min)≦Φ_(mg)≦Φ_(max) the desired value Ic of        the welding intensity is not modified, if Φ_(mg)<Φ_(min) the        desired value Ic of the welding intensity is increased.

It is also possible to fix a value R₀<R_(min) and, if the lastprediction of the diameter of the weld nugget Φ is less than Φ₀, thedesired value Ic of the welding intensity is increased.

It is also possible to fix a welding intensity increment ΔIc and, whenthe desired value Ic of the welding intensity is decreased or increased,the increment ΔIc is subtracted from or added to Ic.

This method is preferably implemented by a computer.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in greater detail for the example ofspot-welding with reference to the accompanying drawings, in which:

FIG. 1 is a basic diagram of the spot-welding of two metal sheets,

FIG. 2 is a schematic sectional view of a spot-weld nugget,

FIG. 3 is a schematic sectional view of a spot-weld nugget after pullingapart,

FIG. 4 is a diagram showing the development of the diameter of the weldnugget as a function of the welding intensity for two states of wear ofthe welding electrodes,

FIG. 5 is a diagram showing the development of the welding intensityinstruction as a function of the number of welds produced,

FIG. 6 shows schematically the development of several characteristicquantities of the welding in the course of producing a spot-weld.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Spot-welding is a method of assembling two metal sheets which is knownper se. Two sheets 1 and 2 (FIG. 1) are disposed one upon the other in amarginal overlap zone and are clamped between two electrodes 3 and 3′connected to a control module 4 having a transformer connected to asource of electricity 5. With the aid of the electrodes an electriccurrent of intensity Ic is made to pass during a limited time throughthe contact zone 6 of the sheets which is situated between theelectrodes. The passage of the electric current in the contact zone 6causes the metal to heat up which makes it melt and form a molten core 7(FIG. 2) surrounded by a zone affected by the heat 8 a which hasindentations 9 and 9′ caused by the pressure of the electrodes. Afterthe passage of the electric current, the molten core 7 solidifies andensures a connection between the two sheets. In general, in order toassemble the two sheets a plurality of spot-welds are produced which aredisposed along the overlap zone of the sheets.

The whole area consisting of the zone which is molten then solidified 7and the zone affected by the heat 8 a is called the weld nugget 8 b(FIG. 3).

The quality of the weld, that is to say the mechanical resistance of theweld nugget, is evaluated by the average diameter of the latter. Inorder to measure this average diameter, a portion of spot-welded sheetscontaining a weld nugget is taken and the two pieces of sheet areseparated by pulling apart. Then (FIG. 3) a portion of sheet 1 acontaining an approximately round hole 10 and a portion 2 a containingthe nugget 8 b are obtained. In order to measure the diameter Φ of thenugget, the largest and the smallest diameter of the nugget are measuredand the arithmetic mean of these two measurements is formed. Thismeasurement is made in the groove 16 which is situated approximately atthe interface between the two sheets. Thus the quality of the weld is ameasurable quantity, the measurement of this quality being the diameterof the weld nugget. It should be noted that the quality of the weld canalso be measured by other means, for example by measuring the force ofpulling apart the weld nugget; the person skilled in the art knows howto determined these methods of measuring the quality of the weld nugget.However, this quantity is not observable in the sense which was definedabove, since in order to measure it it is necessary to destroy the weldand consequently it is not possible to measure it in real time, that isto say as the weld is being produced.

The welding process comprises the following steps:

-   -   putting the sheets in place between the electrodes,    -   docking, an operation consisting of bringing the electrodes        closer to the sheets and progressively clamping them by        increasing the clamping force up to a nominal value,    -   fusion of the molten core by passing current through during a        predetermined time,    -   forging by maintaining the clamping force during a predetermined        time,    -   relaxation of the clamping by moving the electrodes apart.

Each of these steps lasts a fraction of a second or about a second, thecomplete cycle lasting several seconds.

The quality of the welding, for sheets of a given thickness and type(nature of the metal, presence or absence of coating, etc.), dependsupon the following parameters:

-   -   clamping force F of the electrodes against the sheets,    -   intensity of the welding current Is,    -   time during which the current Δt_(s) is made to pass through,    -   time during which the force for forging Δt_(f) is applied,    -   state of wear of the electrodes.

For each of these parameters, except for the state of wear of theelectrodes, desired values are defined which are those which must beproduced with the aid of the welding machine controlled by its automaticsystems.

It will be observed that, at a given clamping force F, a given time forpassage of the current Δt_(s) and a given forging time Δt_(f) thequality of welding (measured by the diameter of the nugget Φ) varieswith the current Is (FIG. 4) starting from a minimum value Φ_(min) andreaching a maximum value Φ_(max) when the current Is passes from a valueI_(min) to a value I_(max), the value above which a phenomenon calledexpulsion is observed corresponding to the fact that the fusion is toogreat so that the molten metal is expelled without the diameter of thenugget increasing; in fact, this latter decreases, as the curve 11indicates.

However, the diameter of the weld nugget also depends upon the wear ofthe electrodes (which is reflected inter alia by an increase in thediameter of the ends of the electrodes). The effect of this wear is todeform the nugget diameter=f (intensity) curve by displacing it towardsthe high intensities and decreasing its gradient, as can be seen in FIG.4, in which the curve 11 corresponds to a new electrode and the curve 12to a worn electrode. For the worn electrode the minimum diameter Φ_(min)corresponds to an intensity I′_(min)>I_(min) and the maximum diameterΦ_(max) corresponds to an intensity I′_(max)>I_(max); the differencebetween I_(max) and I′_(max) being substantially greater than thedifference between I′_(min) and I_(min).

In order for the welding to be satisfactory, it is necessary for thediameter of the weld nugget to be between Φ_(min) and Φ_(max) and forthe intensity to be less than the intensity for which the phenomenon ofexpulsion appears. As the electrodes wear during production of thewelds, in order to guarantee the quality of the successive spot-welds itis necessary at least to make the instruction develop as the number ofspot-welds produced with the same electrodes increases.

FIG. 5 shows a diagram representing “number of welds/intensity” in whichthe curves 13 and 14 are shown which represent respectively thedevelopment of I_(max) and I_(min) as a function of the number of welds(the scale of the horizontal axis corresponding to the number of weldsis arbitrary and is chosen so that the curves 13 and 14 are straightlines, which is purely formal).

The curves 13 and 14 delimit a zone of weldability 15 in which thepoints of operation are located which correspond to the successive weldsreferenced s₁ to s₉. These welds are disposed “in steps”, whichcorresponds to the usual manner of controlling a spot-weldinginstallation, known by the name of “law of phase difference”. As inreality the curves 13 and 14 do not have a conveniently known form, itis appropriate to determine the number of welds after which it isnecessary to modify the intensity instruction and to what extent. It isthe object of the present invention, applied to spot-welding, todetermine automatically when to vary the intensity instruction and byhow much.

In order to aid understanding of the invention, an elementary cycle forcarrying out a spot-weld will now be described in greater detail withreference to FIG. 6.

FIG. 6 shows the development over time of two observable quantities,which are:

-   -   the force F clamping the electrodes against the assembly to be        welded,    -   the spacing z between the electrodes; this spacing is measured        by the distance between two arbitrary reference points A and A′        defined on each of the electrodes (FIG. 1).

These two quantities can be measured in real time with the aid of forceand displacement sensors with which the welding machine is equipped in aknown manner.

Six successive phases are observed in FIG. 6, which are:

-   -   1: before clamping of the electrodes the force is zero and the        spacing has a value z₀ which is sufficient to permit positioning        of the sheets to be assembled between the electrodes,    -   2 and 3: docking, the electrodes move towards one another until        they arrive in contact with the sheets, the distance z        decreases, then the force increases to reach the desired force        F_(c) and the distance z is established at a value z₁        corresponding to the contact of the two sheets on one another,    -   4: welding, the electric current is made to pass through with a        desired intensity Ic. During this phase, due to the expansion of        the sheets resulting from the heat generated by the electric        current, the force F increases up to a value F_(max,s), the        spacing z between the electrodes increases up to a value z₂,    -   5: forging, the force is maintained but the supply of electric        current is cut off, the force stabilises at the value F_(c) and        the electrodes move towards one another slightly forming        indentations in the zones of contact with the sheets, the        distance z passes through a minimum z₃,    -   6: end of welding, the electrodes are moved apart in order to        disengage or displace the sheets.

It can also be seen in this drawing that the quantities F and z varywith time.

At each moment F(t) and z(t) can be measured. Using electricalmeasurements which are known per se, it is also possible to measure themomentary intensity i(t) and the momentary voltage u(t) during the phase4.

In order to control the welding process, the desired values are fixedwhich are the force Fc and the intensity Ic as well as the durations ofwelding Δt_(s) and of forging Δt_(f). By suitable computer processing,which the person skilled in the art will know how to carry out, of themeasurements F(t), z(t) and u(t) it is possible to determine, aftercarrying out a spot-weld, quantities which are observable in the sensewhich has been defined above.

These observable quantities are for example:

-   -   the maximum welding force F_(max,s),    -   the maximum expansion in the course of welding Δz_(max,s)=z₂−z₁,    -   the maximum shrinkage in the course of forging Δz_(max,f)=z₂−z₃,    -   the total electrical energy consumed E_(élec)=∫ u(t).i(t).dt,        (the integration is made over the duration of the welding).

It should be noted that in this process the observable quantities whichhave just been defined are not input quantities nor output quantitiesnor desired values.

On the basis of these observable quantities, and particularly on thebasis of the quantities Δz_(max,s), Δz_(max,f) and E_(élec), it ispossible to calculate a forecast value of the diameter Φ_(p) of the weldnugget. In order to calculate Φ_(p) a model M is used which as variablesthe observable quantities Δz_(max,s), Δz_(max,f) and E_(élec), and suchthat:Φ_(p) =M(Δz_(max,s), Δz_(max,f) , E _(élec)).

In this example, and reverting to the terminology defined above, thequantity Φ represents the result R. The model M takes into account thethree observable quantities ΔZ_(max,s), ΔZ_(max,f) and E_(élec), but itcould take other into account and it could involve one or severaldesired values such as Ic, Fc, Δt_(s) and Δt_(f). It is important,however, to note that the model takes into account at least twoindependent variables, of which at least one is an observable quantity,which is necessary in order to evaluate Φ_(p). In effect, taking intoaccount of only one of these measurable quantities, completed if need beby taking into account of one or several desired values, or simplytaking into account of the desired values, does not enable Φ_(p) to beevaluated with sufficient precision.

As has been indicated previously, the control of the spot-weldingprocess consists of determining, after each production of a weld, thedesired values to be applied in order to carry out the following weld ina satisfactory manner. More particularly, it consists of determining thedesired value Ic of the current intensity so that the diameter of theweld nugget is satisfactory, that is to say it is within the two valuesΦ_(min) and Φ_(max) defined above, and so that the desired value Ic ofthe current is situated within the weldability range.

Thus for each welding operation:

-   -   the observable parameters necessary in order to determine the        observable quantities used by the model M are recorded; in the        present case these are Δz_(max,s), Δz_(max,f) and E_(élec),    -   with the aid of the model M an estimate of the result R_(es) is        calculated, equal in the present case to the diameter of the        weld nugget: R_(es)=Φ_(p)=M(Δz_(max,s), Δz_(max,f), E_(élec)),    -   with the aid of a control law L having as input variable at        least R_(es), the desired value of the current Ic is calculated        for the following welding operation: Ic=L(R_(es)),    -   and the following welding operation is carried out using the new        desired value of the intensity.

Several control laws are possible. In particular, it is possible to usethe control law L defined in the following manner:

-   -   a minimum value Φ_(min) and a maximum value Φ_(max) are chosen        for the diameter of the weld nugget,    -   a number qm is chosen,    -   the moving mean Φ_(mg) is formed of qm last predictions of the        diameter Φ of the weld nugget,    -   if Φ_(mg)>Φ_(max) the desired value Ic of the welding intensity        is decreased, if Φ_(min)≦Φ_(mg)≦Φ_(max) the desired value Ic of        the welding intensity is not modified, if Φ_(mg)<Φ_(min) the        desired value Ic of the welding intensity is increased.

It is also possible to fix a value Φ₀<Φ_(min) and, if the lastprediction of the diameter of the weld nugget Φ is less than Φ₀, thedesired value Ic of the welding intensity is increased.

In order to adjust the desired value of the intensity, a weldingintensity increment ΔIc is fixed and, when the desired value Ic of thewelding intensity is decreased or increased, the increment ΔIc issubtracted from or added to Ic.

The model M is a statistical model constructed on the basis of alearning base B_(ap) consisting of all the desired values, theobservable quantities as well as the measurements of the result whichare obtained for a series of N spot-welds. It can be validated on a testbase B_(test) made up in the same way as the learning base but withdifferent examples from those which make up the learning base.

The model M is for example a neural network, but it can be any type ofstatistical model.

The construction of the model and its use will now be described in ageneral manner, then the particular features of the application tospot-welding will be described.

As has been indicated above, the learning base is made up of a set of Nobservations, referenced by an index i, chosen in such a way as to bestcover the possible conditions of carrying out the process to bemeasured.

The following are made to correspond to each observation i:

-   -   the result R_(i) obtained (measured),    -   n variables x^(i) ₁, . . . , x^(i) _(n), corresponding to the        desired values and the observable quantities measured and        forming the vector x^(i); it may be noted that these variables        may equally correspond to input quantities which in the case of        spot-welding may be for example the thickness and the nature of        the sheets to be welded; however, in the present case it is        considered that all the observations are made with identical        sheets.

In the same way, the test base is composed of N′ observations for eachof which the measured values of R and n variables x₁, . . . , x_(n)which constitute the vector x are made to correspond.

The model M is a function of suitable form which the person skilled inthe art will know how to choose as a function of the type of model whichhe wishes to use; this may be a polynomial of the n variables x₁, . . ., x_(n) or a neural network including at least one non-linear neuron anddepending upon the same variables. This function depends upon parametersθ₁, . . . , θ_(q) which constitute a vector θ. It makes it possible tocalculate an estimate of the result R_(est)=M(x; θ) (or in developedfashion: R_(est)=M(x₁, . . . , x_(n); θ₁, . . . , θ_(q))). This modelmay be adjusted on the learning base by seeking the vector θ_(a) whichminimises the score S, also denoted S(M;B_(ap)) when it is calculatedfor the model M on the learning base B_(ap), equal to the sum, for allof the points of the learning base, of the values of a cost function Jwhich is for example the standard deviation between the estimate made bythe model and the result effectively measured:J(x)=(R _(est) −R)² =M(x; θ)−R)²

This cost function J is a function of the variable x which depends uponthe parameters vector θ, so that it can be written in the form J(x₁, . .. , x_(n); θ₁, . . . , θ_(q)).

This then gives:

${S\left( {M;B_{ap}} \right)} = {{\sum\limits_{{i = 1},N}^{\;}{J\left( x_{i} \right)}} = {\sum\limits_{{i = 1},N}^{\;}\left( {R_{{est},i} - R_{i}} \right)^{2}}}$

The vectors x¹, . . . , x^(N) are the vectors corresponding to thedifferent points of the learning base B_(ap). The search for the vectorθ_(a) may be made by any cost minimisation method known to the personskilled in the art, such as for example the quasi-Newton algorithm(described for example in W.H. PRESS & al, “Numerical Recipes in C: Theart of Scientific Computing” second Edition, Cambridge University Press,1992) or the Levenburg-Marquardt algorithm (described for example in K.LEVENBURG, “A Method for the Solution of Certain Non-linear Problems inLeast Squares”, Quarterly Journal of Applied Mathematics II (2), pp.164–168, 1994, and in D. W. MARQUARDT, “An Algorithm for Least-SquaresEstimation of Non-linear Parameters”, Journal of the Society ofIndustrial and Applied Mathematics 11 (2), pp. 431–441, 1963).

Thus an adjusted model M_(a)(x; θ_(a)) is obtained. Such a model can betested on the test base B_(test) by calculating the score S which isequal to the cost function, calculated for the points of the test base:

${{{S\left( {M_{a};B_{test}} \right)} = {\sum\limits_{{i = 1},N^{\prime}}^{\;}{= {F\left( x^{i} \right)}}}};x^{1}},\mspace{11mu}\ldots\mspace{11mu},{x^{N^{\prime}\mspace{11mu}}\mspace{11mu}{belonging}\mspace{14mu}{to}\mspace{14mu} B_{test}}$

The score can equally be calculated, in the same manner, on the learningbase.

However, for one and the same type of model, models may be envisagedwhich include more or fewer parameters. For example, if the model is ofthe polynomial type of the 1^(st) degree or of a higher degree. Equally,if the model is of the neural network type a model may be chosen whichincludes one or several neuron(s). The score of a model dependsparticularly upon the number of parameters, and in particular when thisnumber increases the score decreases, which is desirable since a modelis all the better as its score is low, in so far as there is noover-adjustment. In effect, the measurement results which constitute thelearning or test bases are tainted by errors which introduce a randomnoise. By increasing the number of parameters too much, it is possibleto obtain a model of which the score on the learning base is zero, whichmight appear ideal but which in reality is a defect. In effect, such amodel predicts perfectly not the phenomenon to be modelled but thephenomenon to which is added the noise which has affected the learningbase. As a result the application of such a model to a point notcontained in the learning base will give an a priori result tainted by amajor error.

Moreover, for one and the same type of model, that is to say for a givenalgebraic form and a given number of parameters, the cost functionadmits in the general case several minima, that is to say severalparameters vectors θ_(a). One model corresponds to each of theseparameters vectors.

In order to seek the best model, that is to say the one which will havethe lowest score whilst not being affected by an over-adjustment, it ispossible to use methods which are known per se, such as the methodsknown as “cross validation” or “regularisation”.

However, these methods are not only unwieldy but also they are notalways sufficiently effective. Also, the inventor has devised a newmethod with improved performance over the known methods.

In order to implement this method, the procedure is as follows:

-   -   a model structure is chosen in which the number of parameters        can be chosen arbitrarily,    -   a first adjusted model is determined as indicated above,        including q₁ parameters: M_(a,1)(x; θ_(a,1)), in which θ_(a,1)        is vector of dimension q₁,    -   the Jacobian Z of the model M_(a,1)(x; θ_(a,1)) is calculated.        For this, the functions M_(a,1)(x^(i); θ) are considered in        which it is considered that the parameters vector θ of the model        is variable. The matrix Z is then the matrix having q₁ lines and        N columns of which the terms z_(i,j) are equal to:        z _(i,j) =∂M _(a,1)(x ^(i); θ)/∂θ_(j) at the point θ=θ_(a,1)    -   then for each observation i of B_(ap) the following scalar,        denoted h_(ii), is calculated:        h _(ii)=(z _(i,1) , . . . , z _(i,q1))(^(t) ZZ)^(−1t)(z _(i,1) ,        . . . , z _(i,q1))    -   then, on the learning base a generalised score is calculated of        the model having as the parameters vector θ_(a,1):

${E\left( \theta_{a,1} \right)} = {\sum\limits_{{i = 1},N}^{\;}\left\lbrack {\left( {{M_{a,1}\left( {x^{i};\theta_{a,1}} \right)} - R_{i}} \right)/\left( {1 - h_{ii}} \right)} \right\rbrack^{2}}$

-   -    and a quantity

${\mu\left( \theta_{a,1} \right)} = {\left( {N \cdot q_{1}} \right)^{{- 1}/2}{\sum\limits_{{i = 1},\; N}h_{ii}^{1/2}}}$

-   -    is calculated    -   then in the same manner models are determined which have,        according to choice, different structures or different numbers        of parameters, or which correspond to different minima of one        and the same cost function. Then a series of models M_(a,k) is        obtained with which the quantities E(θ_(a,k)) and μ(θ_(a,k)) are        associated.    -   by comparing the values of E(θ_(a,k)) and μ(θ_(a,k)) the model        M_(a,k) is then determined for which E(θ_(a,k)) is amongst the        smallest values obtained and μ(θ_(a,k)) is maximal. This model        corresponds to the optimal model which is denoted M_(a,opt).        This is the model which is then used in order to effect        regulation of the process.

In order to determine the optimal model it is possible, for example, toproceed in the following manner:

-   -   a plurality of models M_(a,k) are considered for which the        corresponding values of E(θ_(a,k)) and μ(θ_(a,k)) are        calculated,    -   the set consisting of the values of E(θ_(a,k)) is considered,        this set includes a smaller value min[E(θ_(a,k))], and at least        two models are retained of which the values of E(θ_(a,k)) are        closest to min[E(θ_(a,k))], for this any criterion may be used        which the person skilled in the art can determine,    -   the models which have been selected as indicated are considered,        and amongst those models the one for which the value of        μ(θ_(a,k)) is greatest is retained; this model is the model        considered as optimal.

Thus the model having the greatest μ(θ_(a,k)) is chosen from amongst themodels having the smallest E(θ_(a,k)).

It is also possible, using a method which is known per se, to choose a“set of models” consisting of a plurality of models which are acceptablea priori, and each time that it is wished to make a forecast the set ofmodels is used in order to determine the most relevant forecast (see forexample CLEMEN, R. T. “Combining forecasts: A review and annotatedbibliography”, International Journal of Forecasting, Vol 5, pp 559–584,19890.

In the following reference will be made simply to a “model”, but theexplanation which will be given could be transposed mutatis mutandis bythe person skilled in the art to a “set of models”.

The model thus obtained is not necessarily satisfactory, which is thecase in particular when the learning base does not contain enough pointsor when these points are not distributed in a satisfactory manner in thespace for the entries. In order to evaluate the quality of the model andif need be to improve it, the test base can be used. For this, theprocedure is as follows:

-   -   a range of estimation of the standard deviation of the        measurement noise [σ_(min), σ_(max)] is determined a priori by        preliminary tests for the measurement of the result R,    -   then the score of the model M_(a,opt) is calculated on the test        base: S(M_(a,opt); B_(test)) and this score is compared with the        range [σ_(min), σ_(max)]; if σ_(min)<S(M_(a,opt);        B_(test))<σ_(max), it is considered that the model is        satisfactory; in the opposite case, the learning base is        enhanced with one or several points taken from the test base and        the calculation of an optimal model is recommenced.

The examples taken from the test base and introduced into the learningbase can be chosen in various ways. However, it is preferable to choosethe points for which the confidence interval for estimation of theresult R made by the model is the greatest, that is for which thisestimate is the most uncertain. This confidence interval of the point i,irrespective of whether it belongs to the learning base or to the testbase, is determined by the coefficient h_(ii) defined previously. Moreprecisely, it is proportional to h_(ii) ^(1/2). This adjustment orresetting of the model can be made in the course of execution of theprocess, by taking measurements of the result from time to time in sucha way as to constitute a test base with the aid of which the performanceof the model is evaluated and, if necessary, the learning base isenhanced in order to recalculate a model with better performance.

In the particular case of spot-welding, according to the invention:

-   -   by preliminary tests a first learning base is constructed and,        by tests of reproducibility of the measurement, the dispersion        range of the standard deviation of the measurement noise        [σ_(min), σ_(max)] is evaluated for the measurement of the        diameter of the weld nugget (the result R). This learning base        is constructed by producing series of spot-welds with welding        intensities varying alternately between the lower limit of        weldability and the upper limit of weldability without causing        the other desired values to vary, these being the welding time,        the forging time and the welding force. This makes it possible        to construct a model which will serve to control the welding        without varying the duration of a cycle, that is to say        preserving a constant productivity.    -   a statistical model, and preferably a neural model, is        considered, having as input variable the observable quantities        defined above and as output variable the estimate of the        diameter of the weld nugget. With the aid of the learning base,        and by applying for example the method which has just been        defined, the model is optimised. The inventors have found that a        good model is in particular a model of which the input variables        are Δz_(max,s), Δz_(max,f) and E_(élec), as indicated above,    -   in order to regulate the process, the model is used as indicated        above in order to re-update, if necessary, the desired welding        value Ic after each spot-weld is produced.

Furthermore, and in order to improve the model, it is possible duringthe entire duration of operation of the process to take samples ofwelded sheets and to measure the diameter of the weld nugget in such away as to constitute a test base. With the aid of this test base thescore of the model is calculated; if this score is satisfactory themodel is not modified; if this score is not satisfactory the points forwhich the prediction is the most uncertain, that is to say for which theconfidence interval is greater than a value Sk fixed in advance, areextracted from the test base and these points are introduced into thelearning base in order to enhance it. With this enhanced learning basean optimised model is recalculated and the regulation of the process iscontinued with this new model. As will be easily understood, theapplication of the method which has just been described is not limitedto the case of spot-welding but is applicable to any process which maythe subject of modelling.

Irrespective of whether it is applied in the general case or in the caseof spot-welding, the method is implemented by a computer connected tosensors and to a module for controlling the process. This computerincludes programs intended to calculate the optimal model on the basisof files in which are recorded the data relating to the learning andtest bases, programs intended to use the optimal model on the basis ofdata measured over the process, to calculate the desired values on thebasis of the control law, and to send these desired values to theequipment intended to carry out the process. The person skilled in theart will be able to produce such an automatic system.

In the particular case of spot-welding, the equipment intended to carryout the process is a spot-welding machine which is known per se and has,also in a known manner, means for measurement of the position of theelectrodes, the force, the momentary intensity and voltage, as well ascontrol means. These means are connected in a known manner to thecomputer, either directly or by way of particular automatic deviceswhich are known per se.

1. Method of regulating and controlling a technical process which isexecuted in time either in a continuous manner or in a discontinuousmanner by applying at each time t desired values {C₁(t), . . . ,C_(n)(t)} leading to a result R(t) which is measurable but notobservable and generating a plurality of observable quantities separatefrom the result R(t) of which at least two are independent {G₁(t), . . ., G_(m)(t)}, characterized in that: at least two independent observablequantities G₁(t), . . . , G_(p)(t) from the plurality of the observablequantities {G₁(t), . . . , G_(m)(t)}, are measured, with the aid of apredictive model M, or a set of models, of which the variables includethe at least two independent observable quantities, an estimateR_(es)(t)=M(G₁(t), . . . , G_(p)(t)) of the result R(t) is calculated,with the aid of a control law L of which the input variable is theestimated result R_(es)(t), new desired values {C₁(t+1), . . . ,C_(n)(t+1)}=L(R_(es)(t)) are calculated which are applicable for thetime t+1, the desired values {C₁(t), . . . , C_(n)(t)} are replaced bythe desired values {C₁(t+1), C_(n)(t+1)}, and the predictive model M isa statistical adjustment model depending upon parameters {θ₁, . . . ,θ_(p)} which constitute a parameters vector θ adjusted on a learningbase B_(ap) consisting of all of the desired values, the measurements ofthe observable quantities and the measurement of the result for aplurality of successive executions of the technical process.
 2. Methodas claimed in claim 1, characterized in that in order to determine themodel M: a model structure is chosen depending upon a parameter vectorθ, a cost function J is chosen, with the learning base a succession ofadjusted models M_(a,k) is calculated corresponding to differentparameter vectors θ_(k) of dimension q_(k) which minimise, globally orlocally, the cost function on the learning base, for each model M_(a,k)the coefficients h_(ii) of each of the examples of the learning base arecalculated, and the generalised score of the model M_(a,k) iscalculated:${E\left( \theta_{a,k} \right)} = {\sum\limits_{{i = 1},N}^{\;}\left\lbrack {\left( {{M_{a,k}\left( {x^{i};\theta_{a,k}} \right)} - R_{i}} \right)/\left( {1 - h_{ii}} \right)} \right\rbrack^{2}}$and a quantity${\mu\left( \theta_{a,k} \right)} = {\left( {N \cdot q_{k}} \right)^{{- 1}/2}{\sum\limits_{i = {1\mspace{14mu}{to}\mspace{14mu} N}}h_{ii}^{1/2}}}$ is calculated and the model M_(a,k) having the greatest μ(θ_(a,k)) ischosen from amongst the models having the smallest E(θ_(a,k)); thismodel is the optimal model M_(a,opt).
 3. Method as claimed in claim 1,characterized in that: for the measurement of the result R a dispersionrange of the standard deviation of the measurement noise [σ_(min),σ_(max)] is determined, and the parameters {θ₁, . . . , θ_(p)} of thepredictive model M are adjusted in such a way that on a test baseB_(test) it has a score S=S(M; B_(test)) such that σ_(min)<S<σ_(max),the test base consisting of all of the desired values, the measurementsof observable quantities and the measurement of the result for aplurality of successive executions of the technical process.
 4. Methodas claimed in claim 2, characterized in that in order to adjust theparameters {θ₁, . . . , θ_(p)} of the predictive model M, it is possibleto choose a first learning base B_(ap) and a first test base B_(test),with the aid of the said first learning base a first estimate of theparameters {θ₁, . . . , θ_(p)} is determined in such a way that thescore of the model M for the learning base is within the range [σ_(min),σ_(max)], then, using this first estimate of the parameters in the modelM, with the aid of the first test base B_(test), the score S=S(M;B_(test)) is evaluated and compared with the dispersion range [σ_(min),σ_(max)], if S is within the said range it is considered that theestimate of the parameters is satisfactory, in the opposite case thelearning base B_(ap) is completed with examples taken from the firsttest base in order to constitute a new learning base, the test base iscompleted if need be and the parameters {θ₁, . . . , θ_(p)} aredetermined again with the aid of the new learning base and the score Son the new test base, and the iterations are continued until the score Sis within the dispersion range [σ_(min), σ_(max)].
 5. Method as claimedin claim 4, characterized in that in order to complete the learning basewith examples taken from the test base: a confidence interval thresholdSk is fixed for the predictions of the model, the confidence interval Ikfor prediction of the model M is calculated for each of the examples ofthe test base, and at least one of the examples of the test base ofwhich the confidence interval Ik is greater than Sk, that is to say ofwhich the estimate of the result is the most uncertain, is introducedinto the learning base.
 6. Method as claimed in claim 4, characterizedin that the confidence interval Ik of the prediction of the model M foreach example of the test base is proportional to the square root of thecoefficient h_(ii) of this example.
 7. Method as claimed in claim 3,characterized in that in the course of the operation of the process, atleast one result and the corresponding observable quantities aremeasured in such a way as to determine at least one supplementaryexample which is added to the learning base and, with the new learningbase thus obtained, the parameters of the model are adjusted and theperformance of the model is evaluated.
 8. Method as claimed in claim 1,characterized in that the model M is a neural network.
 9. Method asclaimed in claim 1, characterized in that the technical process is thespot-welding of metal sheets.
 10. Method as claimed in claim 9,characterized in that the result R is the diameter Φ of the weld nuggetor any other comparable quantity such as, for example, the force ofpulling apart the weld nugget, and the desired values C₁, . . . , C_(n)are the welding force F_(s), the welding intensity I_(s), the weldingtime Δt_(s) and the forging time Δt_(f).
 11. Method as claimed in claim10, characterized in that the observable quantities are the totalelectrical energy E_(élec), the maximum expansion in the course ofwelding Δz_(max,s) and the maximum contraction during the forging phaseΔz_(max,f).
 12. Method as claimed in claim 10, characterized in that thecontrol law L is defined in the following way: a minimum value Φ_(min)and a maximum value Φ_(max) are chosen for the diameter of the weldnugget, a number qm is chosen, the moving mean Φ_(mg) of the qm lastpredictions of the diameter of the weld nugget Φ is formed, ifΦ_(mg)>Φ_(max) the desired value Ic of the welding intensity isdecreased, if Φ_(min)≦Φ_(mg)≦Φ_(max) the desired value Ic of the weldingintensity is not modified, if Φ_(mg)<Φ_(min) the desired value Ic of thewelding intensity is increased.
 13. Method as claimed in claim 12,characterized in that a value Φ₀<Φ_(min) is fixed and, if the lastprediction of the diameter of the weld nugget Φ is less than Φ₀, thedesired value Ic of the welding intensity is increased.
 14. Method asclaimed in claim 12, characterized in that a welding intensity incrementΔIc is fixed and, when the desired value Ic of the welding intensity isdecreased or increased, the increment ΔIc is subtracted from or added toIc.
 15. Method as claimed in claim 12, characterized in that in order toconstruct a learning base a succession of spot-welds are produced byalternately varying the desired value for the welding intensity Icbetween the lower limit and the upper limit of the range of weldabilityand thus using the welding electrodes, the other desired values beingkept constant.
 16. Method as claimed in claim 1, characterized in thatit is implemented by a computer.